A population of values has a normal distribution with μ = 143.4 and o= 68.3. You intend to draw a random sample of size n = 164. Please show your answers as numbers accurate to 4 decimal places Find the probability that a single randomly selected value is less than 145. P(X < 145) = Find the probability that a sample of size n = 164 is randomly selected with a mean less than 145. P(x < 145) =

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Author:Amos Gilat
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**Question 1**

A population of values has a normal distribution with \( \mu = 143.4 \) and \( \sigma = 68.3 \). You intend to draw a random sample of size \( n = 164 \). Please show your answers as numbers accurate to 4 decimal places.

1. Find the probability that a single randomly selected value is less than 145.
   \( P(X < 145) = \) [Textbox for user input]

2. Find the probability that a sample of size \( n = 164 \) is randomly selected with a mean less than 145.
   \( P(\bar{x} < 145) = \) [Textbox for user input]
Transcribed Image Text:**Question 1** A population of values has a normal distribution with \( \mu = 143.4 \) and \( \sigma = 68.3 \). You intend to draw a random sample of size \( n = 164 \). Please show your answers as numbers accurate to 4 decimal places. 1. Find the probability that a single randomly selected value is less than 145. \( P(X < 145) = \) [Textbox for user input] 2. Find the probability that a sample of size \( n = 164 \) is randomly selected with a mean less than 145. \( P(\bar{x} < 145) = \) [Textbox for user input]
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Step 1

Let random variable X be a population of values.X has normal distribution with mean(μ)=143.4 and standard deviation(σ)=68.3.i.e. X~N(μ,σ)sample size(n) = 164

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